Quasi likelihood analysis of volatility and nondegeneracy of statistical random field

We construct a quasi likelihood analysis for diffusions under the high-frequency sampling over a finite time interval. For this, we prove a polynomial type large deviation inequality for the quasi likelihood random field. Then it becomes crucial to prove nondegeneracy of a key index _χ0${\chi }_0$. By nature of the sampling setting, _χ0${\chi }_0$ is random. This makes it difficult to apply a naïve sufficient condition, and requires a new machinery. In order to establish a quasi likelihood analysis, we need quantitative estimate of the nondegeneracy of _χ0${\chi }_0$. The existence of a nondegenerate local section of a certain tensor bundle associated with the statistical random field solves this problem.